1. Field of the Invention
This invention generally relates to processing images, and more particularly to a system and method for unwrapping a phase difference image in order to produce an image of improved quality and information content.
2. Description of the Related Art
Computed imaging systems are employed in a wide variety of applications, including medical, astronomy and terrain analysis. The images produced by these systems often contain features known as phase wrap. These features diminish the quality of the image and therefore information content which might otherwise be discernable if the features were not present. While the concept of phase wrap is explained below in the specific context of a magnetic resonance imaging (MRI) system, those skilled in the art are aware that phase wrap may occur in other imaging modalities including computer tomography, ultrasound, synthetic aperture radar, and even radio astronomy.
Magnetic Resonance Imaging (MRI) is used to obtain digital images of the internal structure of an object (e.g., the human body) having substantial populations of atomic nuclei that are susceptible to nuclear magnetic resonance (NMR) phenomena. In MRI, a strong magnetic field is used to polarize nuclei in the object. These nuclei are then excited by a radio frequency (RF) signal at a particular NMR frequency. By spatially distributing the localized magnetic fields, and then analyzing the resulting RF responses, an image of relative NMR responses as a function of the location of the nuclei may be generated. Additional processing will allow this image to be displayed on a monitor for analysis by a doctor.
The excitation frequency may be defined by the Larmor relationship, which states that the angular frequency, xcfx890, of the precession of the nuclei is the product of the magnetic field, B0, and the so-called magnetogyric ratio, xcex3, a fundamental physical constant for each nuclear species:
xcfx890=B0xcex3
Accordingly, by superimposing a linear gradient field, Bz=Z Gz, on the static uniform field, B0, which defined Z axis, for example, nuclei in a selected X-Y plane can be excited by a proper choice of the frequency spectrum of the transverse excitation field applied along the X or Y axis. Similarly, a gradient field can be applied in the X-Y plane during detection of free induction decay signals to spatially localize these signals in the plane. The angle of nuclei spin flip in response to an RF pulse excitation is proportional to the integral of the pulse over time.
It is well known that the magnetic resonance phase can serve as a measure of some physical quantity. Depending on the pulse sequence, the MR phase can, for example, represent the main B0 field inhomogeneity which corresponds to phase wrap in the output image.
In order to improve image quality, phase unwrapping is often performed. Phase unwrapping refers to the process of determining the absolute phase of a complex signal given the measurement of its principal phase value. More succinctly, since the phase angle of a complex number is unambiguous only between xe2x88x92xcfx80 and +xcfx80, the phase of an image signal cannot be unambiguously determined from its argument.
In the context of an MRI system, phase unwrapping is a necessary tool for performing three-point Dixon water and fat separation and can be used to increase the dynamic range of phase contrast MR velocity measurements. Phase unwrapping has also been shown to be important in the context of other systems, such as synthetic aperture radar systems. See, for example, U.S. Pat. No. 6,011,625.
Various approaches have been proposed for performing phase unwrapping. One approach is based on a least-squares algorithm which determines the phase surface which best fits the ensemble of pixel-to-pixel phase differences over an interferogram. If inconsistencies are present, the least-squares process attempts to minimize deleterious effects by minimizing the residual fitting error.
Other approaches are based on a path-following algorithm. This algorithm numerically integrates the pixel-to-pixel phase differences over an interferogram, in the process of either avoiding or minimizing inconsistencies by selecting paths where error is minimized.
Another approach used specifically in MRI systems involves a combination of modeling the static magnetic field using polynomial functions as a guided phase unwrapping by region-growing. Such an approach is disclosed, for example, in U.S. Pat. No. 6,263,228.
The phase unwrapping approaches discussed above are either locally applied or remove a low-order approximation of the phase difference image in an effort to make the remaining high-order image wrap-free. By removing low frequencies from an image, some global information is taken into account but the assumption that the remaining high frequencies do not include any phase wraps is frequently incorrect, especially in so-called open MRI systems, and this is true even of geometrically simple phantoms. These techniques do not take into account global information without making a priori assumptions.
Local methods use nearest-neighbor pixels to determine whether a pixel should be unwrapped. Methods of this type are highly sensitive to phase errors. For example, a single pixel with an incorrect phase can cause a wrap to be streaked across the entire image. Local techniques which demonstrate this sensitivity include recursive routines and the Ahn technique, the latter of which streaks when applied column-by-column to two-dimensional phase difference images even when a little noise is present.
Open MRI systems are especially susceptible to image degradation caused by phase errors. Open MRI systems generate phase difference images which are more difficult to unwrap than tranditional cylindrical systems. In particular, the lower field strengths produced by these systems have degraded signal-to-noise ratio in the 0.7T OpenSpeed MRI system and the 0.5T Profile system compared to 1.5T cylindrical systems. Furthermore, fields generated by open MRI systems tend to be less homogenous than cylindrical systems and therefore generate phase difference images with many more wraps to be undone. Additionally, signal-to-noise is far worse in open MRI systems, which produce a larger number of phase errors. Because local unwrapping approaches look only at nearest neighbors when determining whether to unwrap a pixel, they are slow, extremely sensitive to phase errors, and therefore inadequate when applied to open MRI.
Conventional phase unwrapping approaches have also proven inadequate when applied to digital images in which noise is present. For example, because the measurements are corrupted, it is simply impossible to unwrap the image so the all nearest-neighbor pixel differences are smaller than xcfx80.
In view of the foregoing considerations, it is clear that there is a need for an improved method for unwrapping phase difference images including those in which noise is present, and more specifically one which may be applied more efficiently and with fewer errors compared with conventional methods.
The present invention is a system and method for processing digital images more efficiently and with fewer errors than conventional methods. The invention is especially well suited to processing digital images containing noise. The method includes acquiring a phase difference image which includes one or more wraps, creating a modulated phase difference image from the phase difference image, comparing the modulated phase difference image to the phase difference image to locate areas in said phase difference image to be unwrapped, and unwrapping the phase difference image based on the areas located in the comparing step. The modulated phase difference image may be created by rotating the phase difference image by a predetermined angle, and then registering the pixels in the rotated image so that values of the pixels lie within a desired phase range. The desired phase range may equal, for example, a phase range within which pixels of the phase difference image reside. The unwrapping step includes replacing wrapped pixels in the phase difference image with pixels in the modulated phase difference image.
The system of the present invention includes an imaging device, a storage unit for storing an image from the imaging device, and a processor for processing digital images in accordance with the method of the present invention. The processor may perform the method under control of a computer program stored in a memory unit of the system. The various images generated by the invention may be displayed on a monitor or other output device.
The system and method of the present invention is advantageous in a number of respects. One advantage results from the replacement step. Specifically, replacing pixels in the phase difference image with pixels in the modulated phase difference image will have a smoothing effect which will cause the wrapped pixels in the phase difference image to become unwrapped. This is because the replacement pixels in the modulated phase difference image represent rotated pixels in the phase difference image, which suffer no wraps near the phase wrap in the original image. As a result, an image of improved quality and information content is produced.
Further, the image segmentation steps of the invention may be applied to remove inconsistent pixels from the region to be unwrapped. In so doing, phase errors that would severely corrupt results of local phase unwrapping routines are advantageously eliminated. Another advantage is that the method of the present invention takes a global approach to phase unwrapping. This will allow AutoShim to be implemented in an open MRI system, and will make AutoShim more effective in traditional cylindrical MRI systems. Conventional methods cannot achieve these advantages because they are locally applied. The invention also may be applied to a wide variety of images, including magnetic resonance images derived from both cylindrical and open MRI systems, computed tomography images, X-ray images, ultrasound images, and images derived from a synthetic aperture radar system. These and other advantages and features of the invention are described in greater detail in the discussion which follows.